First Order Elliptic Operators on Compact Manifolds

Abstract

We describe the simple first order differential operators on vector bundles over the compact differentiable manifolds. We introduce the Spectral theorem for these operators and apply to prove the Hodge decomposition theorem.;콤팩트인 미분 다양체상에서 simple인 미분 연산자를 소개하고, 이 연산자의 Spectral 정리를 이용하여 Hodge decomposition 정리를 증명한다.